Abstract
This article investigates the consensus tracking control problem of the leader–follower spacecraft formation system in the presence of model uncertainties, external disturbances, and actuator saturation, where the relative motion of the leader and the follower need to track a desired time-varying trajectory given in advance. First, the six-degree-of-freedom relative-coupled translational and rotational dynamics models are derived using the exponential coordinates on the Lie group SE(3). Then, a fast terminal sliding mode control law is proposed to guarantee the tracking control objective come true in finite time robust against all the aforementioned drawbacks. As a stepping stone, an extended state observer is designed to estimate and compensate the total composed disturbances of the system, and it is proved that the estimate errors can converge to a really small neighborhood of the origin in finite time. Based on the observer information, a less-conservative modified controller is furthermore developed to eliminate the chattering caused by the signum function. The stability of the closed-loop system is shown by theoretical analysis. Finally, the validity of the proposed schemes is illustrated through numerical simulations.
Highlights
In recent years, spacecraft formation flying (SFF) as a key technology for realizing many important space missions, such as spacecraft rendezvous and docking, monitoring of the Earth and its surrounding atmosphere, deep space imaging and exploration, space-based interferometry, stereo-imaging, and terrain mapping, has received wide attention.1–4 Since the functionality of a large complex spacecraft can be achieved by the SFF system which consists of multiple simpler distributed ones, the system robustness, control accuracy, flexibility in configuration, and mission cost have all been improved.5–7 In Scharf et al.,8 a survey on the field of SFF was given by dividing the previous synchronization control schemes into five architectures with leader–follower (LF) included
In order to meet the requirements of aerospace missions with high control accuracy, taking spacecraft rendezvous and docking for example, the follower is required to finish large angular maneuver and complicated translational maneuver with respect to the leader simultaneously, while high control accuracy needs to be satisfied, a six-degree-of-freedom (6-DOF) model taking the relative translational motion, rotational motion, and their coupling into consideration is required
This article attempts to design a control scheme on the LF system robust against external disturbances, model uncertainties, and actuator saturation, such that the follower states can converge to the predefined states with respect to the leader in finite time suitable for missions with high accuracy and quick maneuver tracking requirements
Summary
Spacecraft formation flying (SFF) as a key technology for realizing many important space missions, such as spacecraft rendezvous and docking, monitoring of the Earth and its surrounding atmosphere, deep space imaging and exploration, space-based interferometry, stereo-imaging, and terrain mapping, has received wide attention. Since the functionality of a large complex spacecraft can be achieved by the SFF system which consists of multiple simpler distributed ones, the system robustness, control accuracy, flexibility in configuration, and mission cost have all been improved. In Scharf et al., a survey on the field of SFF was given by dividing the previous synchronization control schemes into five architectures with leader–follower (LF) included. An alternative solution to eliminate the couplings in the developed 6-DOF model is output-feedback control design, which has been widely applied such as Wei et al.23,24 Inspired by these facts, this article attempts to design a control scheme on the LF system robust against external disturbances, model uncertainties, and actuator saturation, such that the follower states can converge to the predefined states with respect to the leader in finite time suitable for missions with high accuracy and quick maneuver tracking requirements. With consideration of model uncertainties, external disturbances, and actuator saturation, a 6-DOF relative-coupled translational and rotational dynamics models are derived using the exponential coordinates on the Lie group SE[3].
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